Frame Multipliers and Their Inversion
* Presenting author
Abstract:
Multipliers are operators which allow an intuitive implementation of a time-variant filter. The analysis coefficients of a signal via a given system are modified by pointwise multiplication, and subsequent synthesis stage via a (possibly different) system. Such operators have been used implicitly for some time in signal processing as time-frequency filters, for Gabor systems, and were later extended for general frames. Thus, the theory can be adapted to other transforms, like wavelet, CQT, AUDlets, and others. One of the important questions related to signal modifications is whether it is possible to go back to the original signal. In this talk, first we give a brief introduction to the concept of frame multipliers and consider some examples as a visualization of the multiplier concept. In particular, we present the MULACLAB tool for signal modification, which is part of The Large Time-Frequency Analysis Toolbox. Then we present some results for inversion of frame multipliers, focusing on inverse formulas which allow iterative approaches and implementation.